Finite Math Examples

$\sqrt[4]{64} + \sqrt{18} + \sqrt{50}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $64$ as $2^{4} \cdot 4$ .

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Step 1.1.1

Factor $16$ out of $64$ .

$\sqrt[4]{16 (4)} + \sqrt{18} + \sqrt{50}$

Step 1.1.2

Rewrite $16$ as $2^{4}$ .

$\sqrt[4]{2^{4} \cdot 4} + \sqrt{18} + \sqrt{50}$

$\sqrt[4]{2^{4} \cdot 4} + \sqrt{18} + \sqrt{50}$

Step 1.2

Pull terms out from under the radical.

$2 \sqrt[4]{4} + \sqrt{18} + \sqrt{50}$

Step 1.3

Rewrite $4$ as $2^{2}$ .

$2 \sqrt[4]{2^{2}} + \sqrt{18} + \sqrt{50}$

Step 1.4

Rewrite $\sqrt[4]{2^{2}}$ as $\sqrt{\sqrt{2^{2}}}$ .

$2 \sqrt{\sqrt{2^{2}}} + \sqrt{18} + \sqrt{50}$

Step 1.5

Pull terms out from under the radical, assuming positive real numbers.

$2 \sqrt{2} + \sqrt{18} + \sqrt{50}$

Step 1.6

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 1.6.1

Factor $9$ out of $18$ .

$2 \sqrt{2} + \sqrt{9 (2)} + \sqrt{50}$

Step 1.6.2

Rewrite $9$ as $3^{2}$ .

$2 \sqrt{2} + \sqrt{3^{2} \cdot 2} + \sqrt{50}$

$2 \sqrt{2} + \sqrt{3^{2} \cdot 2} + \sqrt{50}$

Step 1.7

Pull terms out from under the radical.

$2 \sqrt{2} + 3 \sqrt{2} + \sqrt{50}$

Step 1.8

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 1.8.1

Factor $25$ out of $50$ .

$2 \sqrt{2} + 3 \sqrt{2} + \sqrt{25 (2)}$

Step 1.8.2

Rewrite $25$ as $5^{2}$ .

$2 \sqrt{2} + 3 \sqrt{2} + \sqrt{5^{2} \cdot 2}$

$2 \sqrt{2} + 3 \sqrt{2} + \sqrt{5^{2} \cdot 2}$

Step 1.9

Pull terms out from under the radical.

$2 \sqrt{2} + 3 \sqrt{2} + 5 \sqrt{2}$

$2 \sqrt{2} + 3 \sqrt{2} + 5 \sqrt{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $2 \sqrt{2}$ and $3 \sqrt{2}$ .

$5 \sqrt{2} + 5 \sqrt{2}$

Step 2.2

Add $5 \sqrt{2}$ and $5 \sqrt{2}$ .

$10 \sqrt{2}$

$10 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$10 \sqrt{2}$

Decimal Form:

$14.14213562 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$